You are not allowed to use any online resource. Do not try to copy and paste these questions into Google. That is cheating. Doing so will result in an fSTA2023 Test 2 Fall 2020
Name______________________
To receive credit, you must show all work in a clear, coherent fashion. Please circle your
answers.
For questions 1-6, use the following data that compare test scores with hours studying.
Hours
Studying
0 2 4 5 5 6 7
Score 32 55 72 80 82 93 98
1) Using Hours Studying as the explanatory variable, find the regression line.
2) Interpret the slope of the line.
3) Interpret the y-intercept.
4) Predict the score of a student who studied for 5.6 hours.
5) Find and interpret the residual of the student in the table who studied for 4 hours and had a
score of 72.
6) A building has an elevator that can hold at most 8000 lbs. Bob is planning on transporting a
cargo of 50 boxes via the elevator. Bob has determined that the weights of this type of box are
nearly normal, with lbs and lbs. Assume that this sample of 50 boxes meets
the conditions of the Central Limit Theorem.
a) Identify your variable.
b) Describe the distribution of the means of all possible samples of size 50 by naming the
model, the mean, and the standard deviation.
c) Determine what the sample mean will need to be for the 50 boxes to weigh a total of 8000
lbs. (I’m trying to help you. This is easy.)
d) What is the probability that these 50 boxes will weigh too much for the elevator? In other
words, what is the probability that the sample mean is above what you got for part c)? Be sure
to show all work, including a picture.
e) Based on what you determined above, would your ride this elevator with 50 random boxes?
7) According to the National Safety Council (this is real), 27% of car accidents are caused by
drivers distracted by their cell phones. Consider a sample of 120 random accidents. Assume
that the sample meets all conditions for the Central Limit Theorem.
a) Identify your variable.
b) Describe the distribution of the sample proportions of all possible samples of size 120 by
naming the model, the mean, and the standard deviation.
c) Find the for this sample if 35 of the 120 accidents were caused by cell phone use.
d) Find the probability that 35 or more of the 120 accidents were caused by cell phone use. Be
sure to show all work, including a picture.
e) I can’t think of another question to put here, so let’s do this: To get these points, write here
that you pledge to never text while driving.
8) Write down the symbol used to represent each of the following:
a) Sample mean b) Population Mean c) Population Standard Deviation
d) Sample proportion of success e) Population proportion of failure
f) Sample proportion of failure g) Population proportion of success
h) Sample size i) Number of successes in the sample j) Z-score
9) According to Leichtman Research Group, 62% of American households have a Netflix
account. I currently have 183 students.
a) Using the Central Limit Theorem, find the probability that more than 120 of my students have
Netflix in their home. Be sure to show all work, including drawing a picture and defining your
variable.
b) Do you have any concerns about this sample that might make us concerned if the Central
Limit Theorem applies? Explain.
10) On average, it takes children 25 repetitions of a task to learn how to do that task, with a
standard deviation of 5 repetitions. The Tar Creek community is concerned about lead
poisoning from the local environment, so they do a study on 220 local children.
a) Define your variable.
b) Find the Standard Deviation the distribution of all possible samples of size 220.
c) Local officials determine that it takes this sample of 220 children an average of 75 repetitions
to learn a task. Find the Z-score for this result. Note that it is a very large Z-score.
d) If you try to use your calculator to find the probability of the above or more, (using normalcdf),
if will say 0. It’s not actually 0, but it is so small that your calculator calls it 0. What does that tell
you about this sample, and whether the sample looks like the population?
e) How many repetitions would it need to take a sample of children, on average, to be in the
99th percentile?
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